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Geostatistics is a branch of statistics concerned with stochastic processes over continuous domains, with Gaussian processes (GPs) providing a flexible and principled modelling framework. However, the high computational cost of simulating…

Real engineering and scientific applications often involve one or more qualitative inputs. Standard Gaussian processes (GPs), however, cannot directly accommodate qualitative inputs. The recently introduced latent variable Gaussian process…

Solving hydrologic inverse problems usually requires repetitive forward simulations. One approach to mitigate the computational cost is to build a surrogate model, i.e., an approximate mapping from model parameters (input) to observable…

Fast approximations of power flow results are beneficial in power system planning and live operation. In planning, millions of power flow calculations are necessary if multiple years, different control strategies or contingency policies are…

Frequency-magnitude distributions, and their associated uncertainties, are of key importance in statistical seismology. When fitting these distributions, the assumption of Gaussian residuals is invalid since event numbers are both discrete…

This article advocates the use of conformal prediction (CP) methods for Gaussian process (GP) interpolation to enhance the calibration of prediction intervals. We begin by illustrating that using a GP model with parameters selected by…

Gaussian processes (GPs) are a Bayesian machine learning approach widely used to construct surrogate models for the uncertainty quantification of computer simulation codes in industrial applications. It provides both a mean predictor and an…

Gaussian Processes (GPs) are highly expressive, probabilistic models. A major limitation is their computational complexity. Naively, exact GP inference requires $\mathcal{O}(N^3)$ computations with $N$ denoting the number of modeled points.…

The Iterative Closest Point (ICP) algorithm is a crucial component of LiDAR-based SLAM algorithms. However, its performance can be negatively affected in unstructured environments that lack features and geometric structures, leading to low…

Differential equations are important mechanistic models that are integral to many scientific and engineering applications. With the abundance of available data there has been a growing interest in data-driven physics-informed models.…

The Gaussian process (GP) is a widely used probabilistic machine learning method with implicit uncertainty characterization for stochastic function approximation, stochastic modeling, and analyzing real-world measurements of nonlinear…

By analyzing the Japan Meteorological Agency (JMA) seismic catalog for different tectonic settings, we have found that the probability distributions of time intervals between successive earthquakes --interoccurrence times-- can be described…

Accurate forecasting of multivariate time series remains challenging due to the need to capture both short-term fluctuations and long-range temporal dependencies. Transformer-based models have emerged as a powerful approach, but their…

Volcano eruption forecast remains a challenging and controversial problem despite the fact that data from volcano monitoring significantly increased in quantity and quality during the last decades.This study uses pattern recognition…

We here consider the subset simulation method which approaches a failure event using a decreasing sequence of nested intermediate failure events. The method resembles importance sampling, which actively explores a probability space by…

Gaussian processes (GPs), or distributions over arbitrary functions in a continuous domain, can be generalized to the multi-output case: a linear model of coregionalization (LMC) is one approach. LMCs estimate and exploit correlations…

As one of the leading causes of mortality and disability worldwide, Acute Ischemic Stroke (AIS) occurs when the blood supply to the brain is suddenly interrupted because of a blocked artery. Within seconds of AIS onset, the brain cells…

Gaussian processes (GPs) are a popular class of Bayesian nonparametric models, but its training can be computationally burdensome for massive training datasets. While there has been notable work on scaling up these models for big data,…

Gaussian Process (GP) regression is a flexible modeling technique used to predict outputs and to capture uncertainty in the predictions. However, the GP regression process becomes computationally intensive when the training spatial dataset…

Gaussian processes (GPs) are widely used as distributions of random effects in linear mixed models, which are fit using the restricted likelihood or the closely-related Bayesian analysis. This article addresses two problems. First, we…